Gadolin graduated the Mikhail Artillery School in 1849 and remained their to teach. He developed techniques for building high velocity canons, which significantly increased the range a shell could be propelled. He is remembered in crystallography for deriving the 32 macrosymmetrical crystal groups, and devising a method for depicting these groups on a sphere that is still in use to the present. The St. Petersburg Academy of Sciences awarded him the Lomonosov prize for his crystallographic work, 1868.

Extremely rare. This is the separate appearance of Gadolin's Deduction of all Crystallographic Systems and their Subdivisions by Means of a Single General Principle that showed there are only a limited number of possible crystallographic polyhedra possible. In 1830 Carl Friedrich Naumann coordinated the crystallographic systems of Weiss and Mohs, but which to some degree ignored symmetry elements. In response Gadoin who was a Russian artillery professor and a talented amateur crystallographer became agitated over Naumann's lack of rational in developing his crystallographic descriptions. To better relate symmetry and crystallography Gadolin developed his own procedure for studying crystal symmetry.

Beginning with the empirical law of rational parameters Gadolin demonstrates in this work that it is possible to derive through deduction all the crystallographically possible polyhedra by studying how the elements of symmetry can be combined. In this way Gadolin shows that the resulting polyhedra can be divided into 32 classes varying by symmetry. He also states unequivocally and for the first time that two crystals should belong to the same crystal class if they have the same elements of symmetry. This is the foundation of modern classification into geometric crystal classes.

Like some other scientific works this revolutionary work was largely overlooked at the time of its publication. It was only in later years that Gadolin's crystal classes became generally accepted and led to many significant theories and practical studies. Even today and to the consternation of many student geologists the Gadolin classification is to be found worked out in many mineralogical textbooks.

Scarce. Edited by Paul Groth, this is a German translation of Gadolin's famous crystallography. It is the first appearance in book form in a European languge although it appeared after a French rendering that originally appeared in Acta Societatis Scientiarum Fennicae, Helsingfors, 9 (1871). This German edition was published as volume 75 of Ostwald's famous series of translations.